Methods and systems for numerical prediction and correction of processes using sensor data

ABSTRACT

Methods and systems are disclosed for simulating a fabrication process based on real time sensor measurements obtained during the process. In one embodiment, a first simulation of the process computes a set of predicted physical responses based on a first set of assumed boundary conditions, and then, during the fabrication process sensor measurements are obtained and used to compute a second set of boundary conditions. A second simulation, based on the second set of boundary conditions, can then be performed to compute an updated set of predicted physical responses that can be compared to the previously computed set of physical responses. The difference(s) can be used to determine line, surface or volumetric response distribution from point, line or surface boundary conditions respectively, whether and how to modify the fabrication process (or other processes) and how to take additive and other manufacturing process decisions real-time using simulation. Other examples are also described.

This application claims the benefit and filing date of U.S. ProvisionalPatent Application No. 62/886,257, filed Aug. 13, 2019, and thisprovisional patent application is hereby incorporated herein byreference.

BACKGROUND

Existing simulation methods have been used to simulate fabricationprocesses. For example, simulation software from ANSYS, Inc. has beenused to simulate additive manufacturing (AM) processes. AM processes canbe performed by a 3D printer, and a 3D printer can fabricate an objectin a layer by layer process. In this process a layer of powder, such asa metallic powder, is applied through a nozzle to an object beingfabricated, and then the powder is selectively melted by the 3Dprinter's laser (or other energy source) and then the melted materialcools and solidifies into a shaped layer on the object that is beingfabricated. The speed of the powder extruded through the nozzle can becontrolled during the AM process. Then another layer of powder can beapplied and the process can be repeated (for example, selective meltingfollowed by cooling, etc.). Existing simulation methods and models allowan additive manufacturing process to be simulated from start to finishto reveal, based on the assumptions and inputs provided to thesimulation models, the predicted properties of the finished object, suchas shape, size of portions of the object, etc. If the predictedresponses do not match a desired set of thermomechanical responses, thesimulation can be repeated with different assumptions and inputs toproduce another set of predicted properties, and this can be repeateduntil the predicted responses converge to an adequate match of thedesired set of responses. The outputs from a simulation that produces anadequate match can be used to provide control parameters to a 3Dprinter. If the set of assumptions and inputs do not accurately reflectactual physical systems, many iterations of the simulation may berequired.

SUMMARY OF THE DESCRIPTION

According to one aspect described herein, a simulation of a process canuse real-time sensor measurements to provide boundary conditions andcreate a simulation that predicts results of the process based on thereal-time sensor measurements so that the results are based on actualphysical properties using, for example, a CALPHAD approach that uses thesensor measurements. The sensor measurements can be captured by sensorsin real time during the process, such as in the middle of the processbefore the process is completed, and the sensor measurements can be usedto create updated inputs or assumptions that are based on the sensormeasurements and are different than the initial inputs or assumptionswhich were used in an initial simulation of the process. The updatedinputs or assumptions, such as boundary conditions, can then be used ina subsequent simulation to predict results, such as evolvingtemperatures and deformations of the process. These predicted resultscan be compared to desired results and the comparison can inform how tomodify the process either as the process continues or in a new processthat is started with modified control parameters that are based on thesubsequent simulation. The process can be used, for example, tofabricate an object or part using an AM process. For example, thecontrol parameters of an additive manufacturing process can be correctedor modified for the current and future additive manufacturing layers onthe fly using the error between the expected and real time volumetricdata provided by the initial simulation and the subsequent simulation.The initial simulation and the subsequent simulation can use, in oneembodiment, a finite element solver that uses voxels to mesh the part inan STL file, and the top surface configuration of the voxels can bematched to the positions of sensor measurements that are collectedacross the surface, for example by an FLIR sensor, so that each of thetop surface voxels of the part has a sensor measurement associated withit; for example, one embodiment can match an exposed surface, line orpoint of one or more sensor measurements such as temperature ordisplacement (e. g., movement), either a one-time measurement or a timeseries set of measurements, with a sliced CAD surface such as a slicedSTL surface. According to another aspect, an embodiment can projectresults from the subsequent simulation, such as results from the voxelson a mesh grid, to be mapped to an augmented reality display device. Theaugmented reality display in one embodiment can display informationshowing how the design has changed as a result of modifications of theprocess.

In one embodiment, a method for improving a fabrication process caninclude the following operations: performing a first simulation of afabrication process using available process simulation methods andassumed boundary conditions, where the first simulation computes a firstset of results to define predicted physical volumetric responses such astemperatures and deformations for a first object to be created in thefabrication process and wherein the first set of results are based on afirst set of one or more boundary conditions; receiving, from one ormore sensors, sensor measurements of one or more parameters that aresensed by the one or more sensors during the fabrication process afterthe fabrication process has been initiated; performing a secondsimulation based on the sensor measurements, the second simulationcomputing a set of results based on the sensor measurements and based ona set of boundary conditions that are based on the sensor measurements;and storing the set of second results for use in performing a modifiedfabrication process. In one embodiment, the modified fabrication processcan be a continuation of the fabrication of the first object afterreceiving the sensor measurements. In one embodiment, the method canfurther include outputting the second set of results to drive themodified fabrication process for the continued fabrication of the firstobject. In one embodiment, the modified fabrication process can be usedto fabricate a second object after the first object was fabricated orafter its fabrication was aborted. In one embodiment, the method canfurther include the operation of: comparing the first set of results tothe second set of results to determine a degree of discrepancy of atleast one of temperature or displacement of one or more simulated nodeson a mesh in a finite element analysis or computational fluid dynamicssimulation of the first object.

In one embodiment, the method can further include the operation of:dynamically updating the fabrication process as it occurs withoutstopping it to create the modified fabrication process based on thedegree of discrepancy. In one embodiment, the fabrication process caninclude an additive manufacturing process, and wherein information aboutthe first object is stored in a computer automated design file having anSTL file format. In one embodiment, the method can further include theoperation of: matching a sensed position on the first object during thefabrication process with a location, such as a voxel or node, in thecomputer automated design file.

In one embodiment, the first set of boundary conditions (assumed) andthe second set of boundary conditions (based on real-time capture ofstimuli such as temperature or displacements on the exposed surfaces)are constraints used for the solution of one or more differentialequations which are solved in the first simulation and the secondsimulation respectively.

In one embodiment, the sensor measurements can comprise image data ofthe first object, and the image data is used to derive displacement datafor nodes on the top surface of the object or other surfaces based ontheir exposure availability.

In one embodiment, the sensor measurements can include temperature datafor locations on the first object during the fabrication process, andthese locations are matched to the position of each node or voxel in aset of nodes or voxels in at least the second simulation. The sensormeasurements can also include position data for a set of nodes orvoxels, wherein this position data can show displacements or movementsof voxels as a result of the fabrication process.

In one embodiment, the method can further include the operation ofoutputting display data to an augmented reality display, where thedisplay data is based on the second set of results. This display datacan be displayed on a head mounted display (or other display device).

The aspects and embodiments described herein can include non-transitorymachine readable media that store executable computer programinstructions that when executed can cause one or more data processingsystems to perform the methods described herein when the computerprogram instructions are executed by the one or more data processingsystems. The instructions can be stored in nonvolatile memory such asflash memory or dynamic random access memory which is volatile or otherforms of memory.

The methods, systems, and non-transitory machine readable storage mediadescribed herein can also be extended beyond fabrication processes sothat the one or more embodiments described herein can be used in othercontexts in which computer modeling can be used to simulate or representphysical systems or physical processes. For example, these othercontexts can include: (a) real-time volcanic finite element analysisthat can model and predict mechanical responses from volcanic systemsbased on sensor measurements that can be used to compare to a priorsimulation or model of the volcanic system; (b) mechanical systemshaving contact interfaces between components that can produce boththermal and mechanical responses over time based on simulated inputs;and (c) optical responses from optical sensors used in, for example,driving or assisted driving.

These other contexts can also include the use of embodiments to detectand potentially mitigate defects in, for example, an object beingcreated during a fabrication process, such as an additive manufacturingprocess. These other contexts can also include embodiments in whichvolumetric temperatures from, for example, a simulation can be used topredict thermal strain which can be used to compute residual stressesand displacements. Another context can include embodiments that useacoustic boundary conditions that are solved for (e.g. in a secondsimulation). Another context can involve embodiments in which thesimulations involve car crashes and the sensor(s) measure thermal anddisplacement values during a car crash on a real physical car and thenthese sensor(s) measurements can be used to continue the simulation ofthe crash or to predict strain on the car, etc. or to predict how thedesign of the car can be improved to reduce negative effects on the carfrom the crash.

The above summary does not include an exhaustive list of all embodimentsin this disclosure. All systems and methods can be practiced from allsuitable combinations of the various aspects and embodiments summarizedabove, and also those disclosed in the Detailed Description below.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example and notlimitation in the figures of the accompanying drawings in which likereferences indicate similar elements.

FIG. 1 shows, in block diagram form, an example of a 3D printer systemwhich can be used with one or more embodiments described herein.

FIG. 2 shows an example of a simulation system according to one or moreembodiments described herein which can include a 3D printer system aswell as a simulation tool.

FIG. 3 is a flowchart which illustrates a method according to oneembodiment described herein.

FIG. 4 is a flowchart which illustrates a method according to oneembodiment described herein.

FIG. 5 is a flowchart which illustrates a method according to oneembodiment described herein.

FIG. 6A is a flowchart which illustrates a method according to oneembodiment which can be used in conjunction with the method shown inFIG. 6B.

FIG. 6B is a flowchart which illustrates a method according to oneembodiment which can be used in conjunction with the method shown inFIG. 6A.

FIG. 7 is a block diagram of a data processing system that can performor implement one or more embodiments described herein; for example, thedata processing system in FIG. 7 can be used to implement the dataprocessing system 101 shown in FIG. 1 or can be used to implement thesimulation tool 207 shown in FIG. 2.

FIG. 8 shows an example of a graphical user interface that shows anaugmented reality display of an object after a second simulation, usingreal time sensor measurements from the object, provides updatedvolumetric temperature distribution data based on those real time sensormeasurements.

FIG. 9 shows a thermal image that was captured by a thermal sensor (e.g.an FLIR sensor).

FIG. 10 (“Edge Image”) shows a processed thermal image after the thermalimage in FIG. 9 is processed with conventional edge detection filters.

FIG. 11 shows a rectangular contour fitted or identified around at leasta portion of the part or object in the fabrication process.

FIG. 12 shows an enlarged view of a portion of FIG. 11.

FIG. 13 shows, in two views (left and right views), the differences inboundary conditions between a first simulation (using assumed boundaryconditions) and a second simulation (using boundary conditions derivedfrom sensor measurements); the left view shows the assumed boundaryconditions that were used for the first simulation and the right viewshows the real boundary conditions derived from one or more sensormeasurements.

FIG. 14 shows an example of how a fabrication process can be changedbased upon the results from the second simulation that is based onsensor measurements.

FIG. 15 shows, in two views, an example of how a defect can be detected(e.g. during a fabrication process) and then mitigated according to anembodiment.

FIG. 16 shows, in two views, an example of how a defect can be detectedand then mitigated according to an embodiment.

FIG. 17 shows an example of how an embodiment can be used to predictthermal strain which in turn can be used to compute residual stressesand displacements

DETAILED DESCRIPTION

Various embodiments and aspects will be described with reference todetails discussed below, and the accompanying drawings will illustratethe various embodiments. The following description and drawings areillustrative and are not to be construed as limiting. Numerous specificdetails are described to provide a thorough understanding of variousembodiments. However, in certain instances, well-known or conventionaldetails are not described in order to provide a concise discussion ofembodiments.

Reference in the specification to “one embodiment” or “an embodiment”means that a particular feature, structure, or characteristic describedin conjunction with the embodiment can be included in at least oneembodiment. The appearances of the phrase “in one embodiment” in variousplaces in the specification do not necessarily all refer to the sameembodiment. The processes depicted in the figures that follow areperformed by processing logic that comprises hardware (e.g. circuitry,dedicated logic, etc.), software, or a combination of both. Although theprocesses are described below in terms of some sequential operations, itshould be appreciated that some of the operations described may beperformed in a different order. Moreover, some operations may beperformed in parallel rather than sequentially.

The methods and systems described herein can use simulations andmeasurements that can be used to improve a process for fabricating anobject, such as an additive manufacturing process. The simulations andmeasurements can be performed during the process to determine thevolumetric response distributions and whether to modify the process (onthe fly) while the process continues to finish fabrication of the objectunder consideration or to create modified control parameters for afuture process that fabricates a second object. In one embodiment, a 3Dprinter can be used in the process to fabricate an object using, forexample, an additive manufacturing (AM) process. FIG. 1 shows an exampleof a 3D printer.

Referring now to FIG. 1, a 3D printer system 100 can include a dataprocessing system 101 that retrieves, from storage 103, the CAD(computer automated design) file that specifies data that is used by the3D printer to control the energy source 105 and the scanner 107 tocreate the object 109. The CAD file may specify data used to create theobject 109 using an AM process, and the data processing system 101interprets the file so as to make decisions about how to run and controlthe energy source 105 and the scanner 107. In one embodiment, the CADfile can be converted to an STL file format which is a known file formatfor use in computer aided manufacturing and in 3D printing. The energysource 105 provides, in one embodiment, heat that is directed towardsthe object 109 through the scanner 107. In one embodiment, the energysource 105 can be a laser which generates a beam of energy that can bedirected to a point or spot on the object based upon how the scanner 107controls the positioning of the laser beam. The laser beam can bescanned in a pattern across the object 109 to selectively melt portionsof the powder to create a new layer on top of the object 109. In anotherembodiment, the energy source may be an electron beam which is alsocontrolled by a scanner to direct the electrons towards the object, suchas object 109, which is being manufactured. In some embodiments, theenergy source 105 may be one or more energy sources that may generateone or more types of energy that can be directed towards an object beingfabricated. The 3D printer system 100 shown in FIG. 1 can be used in theone or more embodiments described herein which use one or more sensorsduring the fabrication process to provide sensor measurements to asimulation tool which can then use those sensor measurements to performan updated simulation as described herein.

FIG. 2 shows an example of a system 201 which can include a 3D printersystem 203 and one or more sensors 211 as part of the system 201 thatcan use sensor measurements obtained during the fabrication process. The3D printer system 203 shown in FIG. 2 can be, in one embodiment, thesame as the 3D printer system 100 shown in FIG. 1. The 3D printer system203 can be coupled to storage, such as a hard drive or flash memorywhich contains the CAD design 205. The CAD design 205 can in oneembodiment be an STL file that specifies geometry data and otherinformation about the object to be fabricated. The simulation tool 207can be a system, such as a data processing system configured withsimulation software that can perform one or more of the methodsdescribed herein such as the use of sensor measurements in order toperform an updated simulation based upon sensor measurements obtainedfrom one or more sensors, such as one or more sensors 211 which arecoupled to the simulation tool 207 and these sensor measurements can beconverted to appropriate boundary conditions. The simulation tool 207can be coupled to receive the CAD design 205 in order to perform atleast some of the methods described herein, such as the method shown inFIG. 4 which is further described below. The 3D printer system 203 canbe controlled based upon the CAD design 205 and control parameters fromthe simulation tool 207 to create the object 209. The fabricationprocess can begin in one embodiment with an initial set of inputs andassumptions based upon an initial simulation by the simulation tool 207,and then the fabrication process can be altered on the fly during theprocess before the process has been completed based upon one or moresensor measurements from the one or more sensors 211 which provide datato the simulation tool 207 during the simulation process. In oneembodiment, the simulation tool 207 can provide display data orinformation to an augmented reality display device 209. In oneembodiment, the augmented reality display device 209 can be aheadmounted display or glasses that allow the user to wear the display.The display device 209 can in one embodiment allow the user to see theobject 109 and also display data about the object including data aboutmodifications to the object that have been made after the simulationtool 207 adjusts the fabrication process on the fly while thefabrication process is ongoing to create the object 109. For example thespeed of the material extruded through a nozzle or the temperature ofnozzle can be adjusted in the middle of the fabrication process basedupon the adjustments made by the simulation tool 207. The system 201 canbe used to perform the methods shown in FIGS. 3, 4, 5, 6A, and 6B in oneembodiment. In one embodiment, the data processing system which controlsthe 3D printer system 203 can include the simulation tool 207 such thatthe simulation tool 207 executes on the data processing system whichcontrols the 3D printer system, such as the data processing system 101.In another embodiment, the simulation tool 207 can execute on a separatedata processing system which is separate from the data processing systemthat controls the 3D printer system 203.

A method according to one embodiment will now be described whilereferring to FIG. 3. In operation 301 in FIG. 3, a data processingsystem can execute a simulation model that has been configured withdefault assumptions, such as default boundary conditions, to obtain aninitial set of predicted physical properties for a first object to befabricated. In one embodiment, this data processing system can includethe simulation tool 207 or be the simulation tool 207 shown in FIG. 2.The simulation model can be implemented in modeling software that usesfinite element analysis methods along with computational fluid dynamicsmethods to generate the predicted volumetric physical responses such astemperature and/or displacements based on accurate properties predictedusing CALPHAD approaches for the first object to be fabricated. Examplesof such modeling software include the ANSYS Additive Suite from ANSYSInc. of Canonsburg, Pa. and 3DSIM. In operation 303, the fabricationprocess can be activated according to the results from the initialsimulation which was performed in operation 301. The results from theinitial simulation can include data that is used to control the 3Dprinting system such as the scan speed of the laser, the power of thelaser, the patterns of the scan for the laser, and the chemicalcompositions of the metallic powders which are available for the 3Dprinting process. In one embodiment, this data can be used to controlthe fabrication process after the fabrication process has been activatedin operation 303. While the fabrication process is being performed afterthe activation in operation 303, one or more sensors, such as one ormore sensors 211 (shown in FIG. 2) can provide sensor measurements to asimulation tool, such as simulation tool 207. This is shown as operation305 in FIG. 3. These sensor measurements can be real time sensormeasurements that can include measurements of temperature and alsoinclude image data such as an infrared image of the object beingfabricated during the fabrication process. In one embodiment, the sensorcan be an FLIR sensor. The temperature data in one embodiment can be aset of temperatures at different points on the surface of the objectbeing fabricated and these points (with corresponding temperaturevalues) can be matched to corresponding positions, such as surface nodesor voxels, in a mesh grid in the simulation model, such as thesimulation model which was executed in operation 301. The simulationtool can then, in operation 307, use the sensor measurement datareceived from operation 305 to compute current boundary conditions ofthe first object based on the real time sensor measurement data andmaterial properties of the object getting printed, for example, thermalconductivity based on the printed material chemical composition. Then inoperation 309, the simulation tool (such as simulation tool 207 shown inFIG. 2), can execute a simulation model again with the simulation modelconfigured with the current boundary conditions computed in operation307 (instead of the default boundary conditions) to obtain a current setof physical responses, such as volumetric nodal degrees of freedom forthe first object. In operation 311, the simulation tool can thendetermine a degree of discrepancy in temperature and/or displacementbased on a comparison between the initial and the current set of surfacedisplacement/temperature conditions. Based on this discrepancy, thesimulation tool in operation 313 can dynamically update the fabricationprocess according to the degree of discrepancy. The method can continuein operation 315 by determining whether or not the fabrication processhas been completed. If it has been completed, then the method is done asshown in operation 317. On the other hand, if the fabrication processhas not been completed then processing can revert back to operation 305to continue monitoring the fabrication process by collecting sensormeasurement data during the fabrication process.

The method shown in FIG. 3 can use the method shown in FIG. 4 in orderto match the sensor measurements captured at different positions on theobject to positions within the CAD file that describes the object beingfabricated. In operation 401, the system can record the position of theenergy source during the fabrication process. In one embodiment, thesepositions may be known from time data and the data file that describesthe data used to control the energy source and the scanner, such as thescanner 107 shown in FIG. 1. In operation 403, sensor measurements arecaptured at each recorded position. Then in operation 405, a simulationtool can match the captured sensor measurements at each position on thesurface or line or point with positions in a layer in a 3D design file,such as the positions of nodes or voxels in a sliced surface in an STLfile. By matching the sensor measurements which were captured to thepositions in a layer in the CAD file, the simulation can use actual realtime sensor measurements at positions that correspond to the nodes orvoxels in the mesh grid used in the simulation to provide an updatedsimulation that reflects the current physical properties of the objectbeing fabricated. This is shown as operation 407. In operation 407,these sensor measurements that have been matched or associated withlocations in the mesh grid are used in updated simulation processes torecompute predicted physical properties for the object in thefabrication process.

In one embodiment, outputs from the simulation process can be providedto an augmented reality display device in order to display data aboutthe object being fabricated during the fabrication process. FIG. 5 showsan example of a method which provides such data to an augmented realitydisplay device. In operation 501, a first simulation of the fabricationprocess can be performed using default or initial assumptions, such asdefault boundary conditions and then the fabrication process can beinitiated. In operation 503, a second simulation can be performed duringthe fabrication process to produce a second set of results, wherein thesecond set of results are based on sensor measurements during thefabrication process and are based on a recomputed set of boundaryconditions that are based on the sensor measurements. Then in operation505, the system can provide display data to an augmented reality (AR)display device, where the display data is based upon the second set ofresults that show how the object will deviate from the initial designbased upon the sensor measurements and based upon adjustments to thefabrication process that were made in response to outputs from theupdated simulation. FIG. 8 shows an example of an AR display device thatdisplays a part or object being fabricated and also displays data aboutthe part or object from the second simulation that uses sensor dataobtained from sensors that monitor the fabrication process. In FIG. 8,an AR display device shows a volumetric temperature distribution thatwas solved using a real-time capture of boundary conditions.

The following description will provide a more specific example of oneembodiment while referring to FIGS. 6A and 6B. The method shown in FIG.6A begins after an initial simulation has been performed using assumedboundary conditions. In operation 601 of FIG. 6A, a simulation tool canretrieve the chemical composition for a current layer in the process;for example, data about the chemical composition of a metallic powderused in an additive manufacturing fabrication process can be obtainedfor the current layer that is being used in an ongoing fabricationprocess. In operation 603, the simulation tool can use a non-equilibriumCALPHAD approach to compute thermophysical properties such as thermalconductivity, density and specific heat of finite element voxels basedon centroid temperature and material state and obtained during theongoing fabrication process and based on the chemical composition forthe layer. Examples of non-equilibrium CALPHAD approaches are describedin U.S. patent application Ser. No. 16/457,902 which was filed on Jun.28, 2019 by Deepankar Pal and Abdul Khader Khan, and this patentapplication is incorporated herein by reference. In operation 605, thissimulation tool can calculate a thermal stiffness matrix and can alsocalculate a structural stiffness matrix. Then in operation 607, thesimulation tool can calculate updated thermal boundary conditions, suchas thermal flux values for the voxels in the mesh grid of the simulationmodel of the object being fabricated, based on sensor measurements andbased on the calculated thermal conductivity which was computed inoperation 603. Then in operation 609, the simulation tool can execute anew simulation based on the current thermal boundary conditions toobtain new volumetric thermal distribution (VTD) data. This new VTD datacan be used to calculate the differences between the new VTD data andprior VTD data using assumed boundary conditions, and these differencescan be multiplied by the calculated thermal stiffness matrix to derive achange in thermal flux distribution over the object in the fabricationprocess. This change in the thermal flux distribution can be used tocompute adjustments in process parameters during the fabrication processin order to attempt to match a desired set of results for the objectbeing fabricated, and this is described in conjunction with operation637 described further below.

Referring now to FIG. 6B, in operation 631, image data, if available,for the object in the fabrication process can be used to determinedisplacement values for elements on the mesh, such as voxels used in thesimulation. In one embodiment, the voxels used in the simulation can bematched to locations in the image data showing displacement, such asmovement of a node or other feature on the object which occurred duringthe fabrication process. This movement or displacement can indicate adeviation from desired results, and the method can modify thefabrication process based on this deviation to attempt to return thefabrication process along the path that produces desired results for theobject being fabricated. In operation 633, the simulation tool cancalculate spatial boundary conditions such as values of forces on nodesor voxels or voxels used in the simulation based on the image data. Inone embodiment, this can provide real-time and/or post-fabricationstructural boundary conditions. The simulation tool can then use thereal-time and/or structural boundary conditions to perform a newsimulation configured with these real-time structural boundaryconditions. Based on this new simulation, the simulation tool inoperation 635 can calculate differences in displacements between thecurrently calculated displacements and the previously calculateddisplacements. These differences can be multiplied by the calculatedstructural stiffness matrix (calculated in operation 605) to obtain thenew forces at each of the nodes or voxels or voxels. Then in operation637, the simulation tool can adjust control parameters during thefabrication process based on the differences in forces and thermal fluxthat were calculated in the method shown in FIGS. 6A and 6B. Forexample, in one embodiment, the simulation tool can provide updated datathat adjust the speed of the scanning of the energy source, the scanningpattering of the energy source, the power of the energy source and/orthe layer composition, such as selecting a different metallic powder foruse for a particular layer during the ongoing fabrication process. Theequations and operations for thermal and structural boundary conditionsremains the same, except for a structural part that has 3 degrees offreedom per node making the K matrix (instead of thermal conductivitymatrix-we call it structural stiffness matrix) of size 3 times biggerboth in row and column directions. In addition, the ‘transient’ solutionneed not be computed as for this case the physics constraints will onlyallow ‘quasi-static’ condition to be incorporated so there will not beany structural analogs of ‘specific heat’ matrix for this solution.

The following equations can be used for carrying out the operationsmentioned herein for at least some embodiments:

Thermal Approach (Equations and Operations)

Real-Time Boundary Capture Finite Element Method

The thermal conduction problems can be solved using a Finite Elementmethodology using equations (1-4) as follows:[C]{{dot over (T)}}+[K _(C)]{T}={f}  (1)

where [C] denotes the specific heat matrix and [K_(C)] denotes thethermal conductivity matrix, {T} denotes the temperature which we aresolving for and {f} denotes the flux vector.

If there is a Dirichlet Boundary condition such as temperaturesprescribed at certain M point, line or surface nodes (it should be notedthat there is only 1 degree of freedom per node in thermal FEA problemsdue to the scalar nature of the thermal field), the temperatures in adiscretized domain are stored in the vector {T}_(bc) with non-zerovalues and other zero values of the size NÃ−1. A flux {f}_(tot,bc) iscomputed using the following equation. It should be noted that in oneembodiment we know the temperatures at the bottom of the base plate andtop surface of the part getting fabricated.{f} _(tot,bc)=[K _(C)]{T} _(bc)  (2)The system of equations in (1) is then reduced to N-M with reaction fluxcomputed at the N-M nodes at their respective coordinates using thefollowing equation.{f} _(shortened,bc) =−{f} _(tot,bc)|_(N-M)  (3)The Neumann boundary condition flux {f}_(Neumann,bc)|_(N-M) is thenadded to {f}_(shortened,bc) in the mapped N-M system as follows{f}| _(N-M) ={f} _(shortened,bc) +{f} _(Neumann,bc)|_(N-M)  (4)

For an assumed boundary condition case, the Neumann Boundary case on thetop surface of the part is assumed and the bottom surface temperature isknown. The difference between the Neumann (assumed on top surface) andDirichlet boundary condition (top surface infrared information) ismeasured and then the Temperatures are computed using equations 5-15) inone embodiment.

The {f}|_(N-M) from the mapped N-M system is supplied to (1), leading tothe thermal solution (for steady state-the [C]{{dot over (T)}} portionof the equation (1) is not required unless ‘transient solution’ ismentioned-which is generally the case in metal and polymer additivemanufacturing—although both of the ‘steady state’ and ‘transient’ solvercapabilities are present with a current solver in one embodiment) in themapped N-M system. Once this solution is computed, the thermal solutionalong with Dirichlet condition is back propagated using the inverse N-Mto N map.

Conversion of Infrared Signal to Exposed Point, Line or SurfaceTemperatures

The following equations can be used to first convert the infrared signalfrom the thermal sensor device—(e.g., a FLIR ONE PRO) to point, line orsurface temperatures.

First, atmospheric transmission constants are defined which are usedthroughout the calculation namely A_(T)α₁, A_(T)α₂, A_(T)β₁, A_(T)β₂ andA_(T)X. For the FLIR ONE PRO camera, these constants can be:A _(T)α₁=0.006569A _(T)α₂=0.01262A _(T)β₁=−0.002276A _(T)β₂=−0.00667A _(T)X=1.9  (5)

Second, the transmission through the IR window is computed from IRsignal strength directly in terms of emissivity ε_(wind) andreflectivity ρ_(wind). These parameters are provided as follows:ε_(wind)=1−IR _(strength)ρ_(wind)=0  (6)

Third, the transmission through the air is computed in terms ofatmospheric transmission constants, relative humidity and FLIR ONE PROimage metadata.

$\begin{matrix}{{H_{2}O_{measure}} = {\left( \frac{RH}{100} \right)e^{({1.5587 + {0.06939{ATemp}} - {0.00027816{ATemp}^{2}} + {Â\mspace{11mu} 0.00000068455{ATemp}^{3}}})}}} & (7) \\{\tau = {{A_{T}{{Xe}^{- \sqrt{{OD}/2}}\left( {{A_{T}\alpha_{1}} + {A_{T}\beta_{1}\sqrt{H_{2}O_{measure}}}} \right)}} + {\left( {1 - {A_{T}X}} \right){e^{- \sqrt{{OD}/2}}\left( {{A_{T}\alpha_{2}} + {A_{T}\beta_{2}\sqrt{H_{2}O_{measure}}}} \right)}}}} & (8)\end{matrix}$

Fourth, the raw object was modified based on radiative attenuation fromthe environment (atmospheric, window and reflective) depending onabove-mentioned parameters.

$\begin{matrix}{\mspace{79mu}{{\rho_{{raw}\; 1} = {\frac{{PR}\; 1}{{PR}\; 2\left( {e^{(\frac{PB}{{RTemp} + 273.15})} - {PF}} \right)} - {PO}}}\mspace{20mu}{p_{{raw}1_{-}{attenuation}} = {\left( \frac{1 - E}{E} \right)\rho_{{raw}\; 1}}}}} & (9) \\{\mspace{79mu}{{A_{T_{-}{raw}1_{-}{attenuation}} = {\frac{{PR}\; 1}{{PR}\; 2\left( {e^{(\frac{PB}{{ATemp} + 273.15})} - {PF}} \right)} - {PO}}}\mspace{20mu}{A_{{T\_ raw}\; 1{\_{attenuation}}} = {\left( \frac{1 - {\overset{¨}{I}}_{''}}{E{\overset{¨}{I}}_{''}} \right)A_{{T\_ raw}\; 1}}}}} & (10) \\{\mspace{79mu}{{{Wind}_{raw} = {\frac{{PR}\; 1}{{PR}\; 2\left( {e^{(\frac{PB}{{IRWTemp} + 273.15})} - {PF}} \right)} - {PO}}}\mspace{79mu}{{Wind}_{{raw}_{-}{attenuation}} = {\left( \frac{ɛ_{wind}*{IRT}}{E\tau} \right){Wind}_{raw}}}\mspace{20mu}{\rho_{{raw}\; 2} = {\frac{{PR}\; 1}{{PR}\; 2\left( {e^{(\frac{PB}{{RTemp} + 273.15})} - {PF}} \right)} - {PO}}}}} & (11) \\{\mspace{79mu}{{p_{{raw}\; 2_{-}{attenuation}} = {\left( \frac{\rho_{wind}{IRT}}{E\;\tau} \right)\rho_{{raw}\; 2}}}\mspace{20mu}{A_{T_{-}{raw}\; 2} = {\frac{{PR}\; 1}{{PR}\; 2\left( {e^{(\frac{PB}{{ATemp} + 273.15})} - {PF}} \right)} - {PO}}}}} & (12) \\{\mspace{79mu}{A_{T_{-}{raw}2_{-}{attenuation}} = {\left( \frac{\left( {1 - \tau} \right)IRT}{E\tau^{2}} \right)A_{T_{-}{raw}\; 2}}}} & (13) \\{{Obj}_{raw} = {\frac{{raw}_{data}{IRT}}{E\tau^{2}} - {p_{{raw}1_{-}{attenuation}^{-}}A_{T_{{raw}\; 1{\_ attnuation}}}} - {Wind}_{raw\_ attenuation} - \rho_{{raw}2_{-}{attenuation}} - A_{T_{{raw}\; 2{\_ attenuation}}}}} & (14)\end{matrix}$

Then, we finally compute the temperature at the surface layer comprisingof the top surface of the part from radiance

T ⁡ ( in ⁢ ⁢ a ^ ″ ⁢ f ) = P ⁢ B log ⁡ ( PR ⁢ ⁢ 1 ( PR ⁢ ⁢ 2 ⁢ ( Obj raw + PO ) +PF ) ) ⁢ a ^ ⁢ ″ ⁢ 273.15 ( 15 )

The FLIR ONE PRO metadata is as follows:

AtmosphericTemperature ATEMP Emissivity E IRWindowTemperature IRWTIRWindowTransmission IRT PlanckB PB PlanckF PF PlanckO PO PlanckR1 PR1PlanckR2 PR2 ReflectedApparentTemperature RTEMP RelativeHumidity RHSubjectDistance ODExtraction of Boundary Condition Temperature on Top Surface

First, the Original image is converted to BGR gray image with Bilateralnoise and Canny Edge Detection Filters as shown in FIG. 9. The image inFIG. 9 can be processed with conventional edge detection filters thatdetect edges between adjacent regions in the image and can produce theresult shown in FIG. 10.

Second, the contour of the edge detected image is identified as shown inFIG. 11.

Third, the geometry is cropped to the contour to supply thermalinformation (Tbc top surface data) used in equation (2) as shown in FIG.11. In the example shown in FIG. 11, a rectangular contour is fitted oridentified around the top surface of the part or object in thefabrication process. FIG. 12 shows an enlarged view of a portion of FIG.11; in one embodiment, Tbc can be set at zero for nodes between the topand bottom layers, and with respect to the bottom layer, nodes in thebottom layer can be set to an ambient temperature thermal condition(e.g. room temperature or regulated heater temperature, etc.).

Differences Between Volumetric Solution Using Assumed and Real-timeBoundary Conditions

The following example shows the results obtained using glass transitiontemperature (converted to Neumann Boundary condition) of PLA materialand real-time boundary conditions as shown in FIG. 13.

The left image in FIG. 13 shows the simulation using assumed boundaryconditions (on the top surface), and the right image in FIG. 13 showsthe simulation (e.g. a second simulation) using real boundary conditions(on the top surface) derived from actual sensor measurements.

Note that the image on the right top surface in FIG. 13 doesn't haveconstant temperatures but when the scale is set to glass transitiontemperature maximum in accordance with left image, it apparently appearsso.

Boundary Condition Correction

The following example shows how parameters in a fabrication process canbe changed based upon outputs from a second simulation that used sensormeasurements to compute real boundary conditions. The following examplecan be one embodiment of operation 313 or operation 637 described above.In one embodiment, a couple of parameters which can be changed (forexample in Additive polymeric extrusion based FEA) are speed of theextrude from a nozzle and nozzle temperature. In one embodiment, thespeed of the extrude from the nozzle can be controlled and thetemperature of the nozzle can also be controlled. If we solve for thedifference problem in temperature distribution and understand therelationship such as between nozzle temperature and real temperature(generally 1 to 1-1 degree change in nozzle temperature is linearlyrelated to 1 degree change in difference problem temperature), theproblem can be corrected as a function of process parameters. A similarapproach can be used for real-time structural finite element or metaladditive manufacturing technologies although the process parameters thatare adjusted are power and speed.

We solve for the following change in flux using equations 1-4Δf=−K(T _(assumedNeumanntopsurface_aftersolvingVTD) −T_(realtimetopsurface))

Once solved, the top surface of the Volumetric Temperature Distributionis plotted and the nozzle temperature has to be increased at localpositions shown in FIG. 14 respectively. FIG. 14 shows the change innozzle temperature as a function of location on the top surface. In oneembodiment, the outputs of second simulation are used to determine howto adjust the nozzle temperature during the remainder of the fabricationprocess.

The embodiments described herein can also help with prediction andmitigation of internal defects. In this modality, there are two optionsfor defect identification.

If the defect is already present and could be observed while the thermalcamera is taking an image of layer ‘n−1’. Then, the defect is identifieddirectly. This will be termed ‘Direct Identification’. The directlyidentified defects can be corrected in layers ‘n’ through ‘m’ where m≥nby modifying the fabrication process during the fabrication process.

If the defect is not present at the time of processing layer ‘n−1’ andtherefore couldn't be observed while the thermal camera is taking animage on the same layer but occurs posteriori while processing layer ‘n’and observing it for inappropriate thermal signatures as it relates tolayers 1 through ‘n−1’. Then, an ideal image at layer ‘n+1’ isreconstructed based on the thermal image capture available at layer ‘n’and compared against the thermal image capture available at layer ‘n+1’for defect identification.

Defect mitigation: For defect mitigation, an inverse problem could besolved for acquiring the correct thermal setpoints on the top surfacefor layer ‘n+2’ as shown below in FIGS. 15 and 16.

The volumetric temperatures from embodiments described herein can beused for predicting the thermal strain resulting in in-directcomputation of residual stresses and displacements as shown in FIG. 17.The direct method comprises of recording top surface displacement data.

FIG. 7 shows one example of a data processing system 800, which may beused with one embodiment. For example, the system 800 may be implementedto provide a system 101 as shown in FIG. 1 or a simulation tool 207shown in FIG. 2. Note that while FIG. 7 illustrates various componentsof a device, it is not intended to represent any particular architectureor manner of interconnecting the components as such details are notgermane to the disclosure. It will also be appreciated that networkcomputers and other data processing systems or other consumer electronicdevices, which have fewer components or perhaps more components, mayalso be used with embodiments of the disclosure.

As shown in FIG. 7, the device 800, which is a form of a data processingsystem, includes a bus 803 which is coupled to a microprocessor(s) 805and a ROM (Read Only Memory) 807 and volatile RAM 809 and a non-volatilememory 811. The microprocessor(s) 805 may retrieve the instructions fromthe memories 807, 809, 811 and execute the instructions to performoperations described above. The microprocessor(s) 805 may contain one ormore processing cores. The bus 803 interconnects these variouscomponents together and also interconnects these components 805, 807,809, and 811 to a display controller and display device 813 and toperipheral devices such as input/output (I/O) devices 815 which may betouchscreens, mice, keyboards, modems, network interfaces, printers andother devices which are well known in the art. Typically, theinput/output devices 815 are coupled to the system through input/outputcontrollers 810. The volatile RAM (Random Access Memory) 809 istypically implemented as dynamic RAM (DRAM), which requires powercontinually in order to refresh or maintain the data in the memory.

The non-volatile memory 811 is typically a magnetic hard drive or amagnetic optical drive or an optical drive or a DVD RAM or a flashmemory or other types of memory systems, which maintain data (e.g.,large amounts of data) even after power is removed from the system.Typically, the non-volatile memory 811 will also be a random accessmemory although this is not required. While FIG. 7 shows that thenon-volatile memory 811 is a local device coupled directly to the restof the components in the data processing system, it will be appreciatedthat embodiments of the disclosure may utilize a non-volatile memorywhich is remote from the system, such as a network storage device whichis coupled to the data processing system through a network interfacesuch as a modem, an Ethernet interface or a wireless network. The bus803 may include one or more buses connected to each other throughvarious bridges, controllers and/or adapters as is well known in theart.

Portions of what was described above may be implemented with logiccircuitry such as a dedicated logic circuit or with a microcontroller orother form of processing core that executes program code instructions.Thus processes taught by the discussion above may be performed withprogram code such as machine-executable instructions that cause amachine that executes these instructions to perform certain functions.In this context, a “machine” may be a machine that converts intermediateform (or “abstract”) instructions into processor specific instructions(e.g., an abstract execution environment such as a “virtual machine”(e.g., a Java Virtual Machine), an interpreter, a Common LanguageRuntime, a high-level language virtual machine, etc.), and/or electroniccircuitry disposed on a semiconductor chip (e.g., “logic circuitry”implemented with transistors) designed to execute instructions such as ageneral-purpose processor and/or a special-purpose processor. Processestaught by the discussion above may also be performed by (in thealternative to a machine or in combination with a machine) electroniccircuitry designed to perform the processes (or a portion thereof)without the execution of program code.

The disclosure also relates to an apparatus for performing theoperations described herein. This apparatus may be specially constructedfor the required purpose, or it may comprise a general-purpose deviceselectively activated or reconfigured by a computer program stored inthe device. Such a computer program may be stored in a computer readablestorage medium, such as, but not limited to, any type of disk includingfloppy disks, optical disks, CD-ROMs, and magnetic-optical disks, DRAM(volatile), flash memory, read-only memories (ROMs), RAMs, EPROMs,EEPROMs, magnetic or optical cards, or any type of media suitable forstoring electronic instructions, and each coupled to a device bus.

A machine readable medium includes any mechanism for storing informationin a form readable by a machine (e.g., a computer). For example, amachine readable medium includes read only memory (“ROM”); random accessmemory (“RAM”); magnetic disk storage media; optical storage media;flash memory devices; etc.

An article of manufacture may be used to store program code. An articleof manufacture that stores program code may be embodied as, but is notlimited to, one or more memories (e.g., one or more flash memories,random access memories (static, dynamic or other)), optical disks,CD-ROMs, DVD ROMs, EPROMs, EEPROMs, magnetic or optical cards or othertype of machine-readable media suitable for storing electronicinstructions. Program code may also be downloaded from a remote computer(e.g., a server) to a requesting computer (e.g., a client) by way ofdata signals embodied in a propagation medium (e.g., via a communicationlink (e.g., a network connection)).

The preceding detailed descriptions are presented in terms of algorithmsand symbolic representations of operations on data bits within a devicememory. These algorithmic descriptions and representations are the toolsused by those skilled in the data processing arts to most effectivelyconvey the substance of their work to others skilled in the art. Analgorithm is here, and generally, conceived to be a self-consistentsequence of operations leading to a desired result. The operations arethose requiring physical manipulations of physical quantities. Usually,though not necessarily, these quantities take the form of electrical ormagnetic signals capable of being stored, transferred, combined,compared, and otherwise manipulated. It has proven convenient at times,principally for reasons of common usage, to refer to these signals asbits, values, elements, symbols, characters, terms, numbers, or thelike.

It should be kept in mind, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities. Unlessspecifically stated otherwise as apparent from the above discussion, itis appreciated that throughout the description, discussions utilizingterms such as “receiving,” “determining,” “sending,” “terminating,”“waiting,” “changing,” or the like, refer to the action and processes ofa device, or similar electronic computing device, that manipulates andtransforms data represented as physical (electronic) quantities withinthe device's registers and memories into other data similarlyrepresented as physical quantities within the device memories orregisters or other such information storage, transmission or displaydevices.

The processes and displays presented herein are not inherently relatedto any particular device or other apparatus. Various general-purposesystems may be used with programs in accordance with the teachingsherein, or it may prove convenient to construct a more specializedapparatus to perform the operations described. The required structurefor a variety of these systems will be evident from the descriptionbelow. In addition, the disclosure is not described with reference toany particular programming language. It will be appreciated that avariety of programming languages may be used to implement the teachingsof the disclosure as described herein.

In the foregoing specification, specific exemplary embodiments have beendescribed. It will be evident that various modifications may be made tothose embodiments without departing from the broader spirit and scopeset forth in the following claims. The specification and drawings are,accordingly, to be regarded in an illustrative sense rather than arestrictive sense.

In the foregoing specification, specific exemplary embodiments have beendescribed. It will be evident that various modifications may be made tothose embodiments without departing from the broader spirit and scopeset forth in the following claims. The specification and drawings are,accordingly, to be regarded in an illustrative sense rather than arestrictive sense.

What is claimed is:
 1. A non-transitory machine readable medium storingexecutable program instructions which when executed cause a dataprocessing system to perform a method, the method comprising: performinga first simulation of a fabrication process, the first simulationcomputing a first set of results to define predicted physical responsesbased on thermal properties for a first object to be created in thefabrication process, the first set of results based on a first set ofone or more assumed boundary conditions; receiving, from one or moresensors, sensor measurements of one or more parameters that are sensedby the one or more sensors during the fabrication process after thefabrication process has been initiated; performing a second simulationbased on the sensor measurements, the second simulation computing asecond set of results based on the sensor measurements and based on asecond set of boundary conditions that are based on the sensormeasurements; and storing the second set of results for use inperforming a modified fabrication process.
 2. The medium as in claim 1wherein the modified fabrication process is a continuation of thefabrication of the first object after receiving the sensor measurementsand wherein the thermal properties include CALPHAD properties.
 3. Themedium as in claim 2 wherein the method further comprises outputting thesecond set of results to drive the modified fabrication process for thecontinued fabrication of the first object.
 4. The medium as in claim 1wherein the modified fabrication process is used to fabricate a secondobject after the first object was fabricated or its fabrication wasaborted.
 5. The medium as in claim 1 wherein the method furthercomprises initiating the fabrication process to fabricate the firstobject.
 6. The medium as in claim 1 wherein the method further comprisescomparing the first set of results to the second set of results todetermine a degree of discrepancy of at least one of temperature ordisplacement of one or more simulated nodes on a mesh in a finiteelement analysis simulation of the first object.
 7. The medium as inclaim 6 wherein the method further comprises dynamically updating thefabrication process as it occurs without stopping it to create themodified fabrication process based on the degree of discrepancy.
 8. Themedium as in claim 1 wherein the fabrication process comprises anadditive manufacturing process and wherein information about the firstobject is stored in a computer automated design file having an STL fileformat.
 9. The medium as in claim 8 wherein the method further comprisesmatching a sensed position on the first object during the fabricationprocess with a location in the computer automated design file.
 10. Themedium as in claim 1 wherein the first set of boundary conditions andthe second set of boundary conditions are constraints used for thesolution of one or more differential equations which are solved in thefirst simulation and the second simulation respectively.
 11. The mediumas in claim 1 wherein the sensor measurements comprise image data of thefirst object and wherein the image data is used to derive displacementdata for nodes.
 12. The medium as in claim 1 wherein the sensormeasurements comprise temperature data for locations on the first objectduring the fabrication process, which locations are matched to theposition of each node in a set of nodes in at least the secondsimulation.
 13. The medium as in claim 1 wherein the method furthercomprises outputting display data to an augmented reality display, thedisplay data based on the second set of results.
 14. A methodcomprising: performing a first simulation of a fabrication process, thefirst simulation computing a first set of results to define predictedphysical responses based on thermal properties for a first object to becreated in the fabrication process, the first set of results based on afirst set of one or more assumed boundary conditions; receiving, fromone or more sensors, sensor measurements of one or more parameters thatare sensed by the one or more sensors during the fabrication processafter the fabrication process has been initiated; performing a secondsimulation based on the sensor measurements, the second simulationcomputing a second set of results based on the sensor measurements andbased on a second set of boundary conditions that are based on thesensor measurements; and storing the second set of results for use inperforming a modified fabrication process.
 15. The method as in claim 14wherein the modified fabrication process is a continuation of thefabrication of the first object after receiving the sensor measurementsand wherein the thermal properties include CALPHAD properties.
 16. Themethod as in claim 15 wherein the method further comprises outputtingthe second set of results to drive the modified fabrication process forthe continued fabrication of the first object.
 17. The method as inclaim 14 wherein the modified fabrication process is used to fabricate asecond object after the first object was fabricated or its fabricationwas aborted.
 18. The method as in claim 14 wherein the method furthercomprises initiating the fabrication process to fabricate the firstobject.
 19. The method as in claim 14 wherein the method furthercomprises comparing the first set of results to the second set ofresults to determine a degree of discrepancy of at least one oftemperature or displacement of one or more simulated nodes on a mesh ina finite element analysis simulation of the first object.
 20. The methodas in claim 19 wherein the method further comprises dynamically updatingthe fabrication process as it occurs without stopping it to create themodified fabrication process based on the degree of discrepancy.
 21. Themethod as in claim 14 wherein the fabrication process comprises anadditive manufacturing process and wherein information about the firstobject is stored in a computer automated design file having an STL fileformat.
 22. The method as in claim 21 wherein the method furthercomprises matching a sensed position on the first object during thefabrication process with a location in the computer automated designfile.
 23. The method as in claim 14 wherein the sensor measurementscomprise temperature data for locations on the first object during thefabrication process, which locations are matched to the position of eachnode in a set of nodes in at least the second simulation.
 24. The methodas in claim 14 wherein the method further comprises outputting displaydata to an augmented reality display, the display data based on thesecond set of results.
 25. The medium as in claim 1 wherein the secondsimulation provides data to mitigate a defect detected during thefabrication process.
 26. The medium as in claim 1 wherein the secondsimulation provides data to predict thermal strain, from which residualstress is computed.
 27. A non-transitory machine readable medium storingexecutable program instructions which when executed cause a dataprocessing system to perform a method, the method comprising: performinga first simulation of a first object involved in a process, the firstsimulation computing a first set of results to define predicted physicalresponses based on thermal or other properties for the first object, thefirst set of results based on a first set of one or more assumedboundary conditions; receiving, from one or more sensors, sensormeasurements of one or more parameters that are sensed by the one ormore sensors during the process after the process has been initiated;performing a second simulation based on the sensor measurements, thesecond simulation computing a second set of results based on the sensormeasurements and based on a second set of boundary conditions that arebased on the sensor measurements; and storing the second set of resultsfor use in creating a modified first object or a modified process. 28.The medium as in claim 1 wherein the first object is a car and theprocess includes a car crash.
 29. The medium as in claim 1, wherein thesecond simulation is a simulation of the fabrication process.
 30. Themethod as in claim 14, wherein the second simulation is a simulation ofthe fabrication process.
 31. The method of claim 30, wherein the firstset of boundary conditions and the second set of boundary conditions areconstraints used for the solution of one or more differential equationswhich are solved in the first simulation and the second simulationrespectively.
 32. The medium of claim 27, wherein the first set ofboundary conditions and the second set of boundary conditions areconstraints used for the solution of one or more differential equationswhich are solved in the first simulation and the second simulationrespectively.